Abstract
Next-generation planetary tracking methods, such as interplanetary laser ranging (ILR) and same-beam interferometry (SBI) promise an orders-of-magnitude increase in the accuracy of measurements of solar system dynamics. This requires a reconsideration of modelling strategies for the translational and rotational dynamics of natural bodies, to ensure that model errors are well below the measurement uncertainties.The influence of the gravitational interaction of the full mass distributions of celestial bodies, the so-called figure-figure effects, will need to be included for selected future missions. The mathematical formulation of this problem to arbitrary degree is often provided in an elegant and compact manner that is not trivially relatable to the formulation used in space geodesy and ephemeris generation. This complicates the robust implementation of such a model in operational software packages. We formulate the problem in a manner that is directly compatible with the implementation used in typical dynamical modelling codes: in terms of spherical harmonic coefficients and Legendre polynomials. An analytical formulation for the associated variational equations for both translational and rotational motion is derived.We apply our methodology to both Phobos and the KW4 binary asteroid system, to analyze the influence of figure-figure effects during estimation from next-generation tracking data. For the case of Phobos, omitting these effects during estimation results in relative errors of 0.42% and 0.065% for the bar{C}_{20} and bar{C}_{22} spherical harmonic gravity field coefficients, respectively. These values are below current uncertainties, but orders of magnitude larger than those obtained from past simulations for accurate tracking of a future Phobos lander, showing the need to apply the methodology outlined in this manuscript for selected future missions.
Highlights
For the robust analysis of tracking data from planetary missions, the dynamics of solar system bodies under investigation should ideally be modelled to well below the observational accuracy and precision
Several exceptionally accurate tracking-data types are emerging for planetary missions, such as multi-wavelength radiometric range and Doppler measurements (Dehant et al 2017), same-beam interferometry (SBI) (Kikuchi et al 2009; Gregnanin et al 2012), and interplanetary laser ranging (ILR) (Degnan 2002; Turyshev et al 2010; Dirkx 2015)
We have derived in detail the equations that relate the full two-body gravitational interaction, including all figurefigure effects, to the typical one-body gravity field representation in terms of spherical harmonic coefficients
Summary
For the robust analysis of tracking data from planetary missions, the dynamics of solar system bodies under investigation should ideally be modelled to well below the observational accuracy and precision. For the analysis of these data, dynamical models for natural bodies need to be developed and implemented to beyond the current state-of-the-art of typical state propagation and estimation software. Examples of such software tools are GEODYN (Genova et al 2016), GINS (Marty et al 2009), GMAT (Hughes et al 2014), NOE (Lainey et al 2004), OREKIT (Maisonobe and Pommier-Maurussane 2010) and Tudat (which we use in this manuscript, see Appendix C). In this article we discuss, and present models to mitigate, one of the common challenges that these tools face for the analysis of future planetary tracking data
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